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September 12th, 2018, 10:24 AM   #1
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what is: sin(a+b)/sin(a-b)

is there any simpler way to write this, I already looked at all the trigonometric identities, I couldn't find anything about fractions of sums.

I also try to find:

cos(a-b)+cos(a+b)

how do I do this, is there anything I'm missing?
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September 12th, 2018, 01:01 PM   #2
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You can always write x=a+b and y=a-b., get sin(x)/sin(y) or cps(y)/cos(x). You can't do anything more, since the angles are completely arbitrary.
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September 12th, 2018, 08:23 PM   #3
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sin(a + b) $\ \ $ tan(a) + tan(b)
--------- = ---------------
sin(a - b) $\ \ $ tan(a) - tan(b)

cos(A - B) + cos(A + B) ≡ 2cos(A)cos(B)
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September 13th, 2018, 04:14 AM   #4
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Quote:
Originally Posted by mathman View Post
since the angles are completely arbitrary.
Hold on, I forgot about this:

a = $\displaystyle \epsilon + \alpha$
b = $\displaystyle \epsilon$
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September 13th, 2018, 04:16 AM   #5
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Quote:
Originally Posted by skipjack View Post
sin(a + b) $\ \ $ tan(a) + tan(b)
--------- = ---------------
sin(a - b) $\ \ $ tan(a) - tan(b)

cos(A - B) + cos(A + B) ≡ 2cos(A)cos(B)

That's nice, thank you!
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September 13th, 2018, 01:39 PM   #6
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Quote:
Originally Posted by theHeavyLobster View Post
Hold on, I forgot about this:

a = $\displaystyle \epsilon + \alpha$
b = $\displaystyle \epsilon$
Are $\alpha$ and $\epsilon$ related? If not, you have a simple change of variables with no more information.
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September 14th, 2018, 02:08 PM   #7
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Quote:
Originally Posted by mathman View Post
Are $\alpha$ and $\epsilon$ related? If not, you have a simple change of variables with no more information.
Ah, yeah you're right. No alpha and epsilon are unrelated.
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